Lab Workbook Page 37 Lab 5: Understanding Normal and Random DataObjective:In this lab, you will use some additional graphical tools to summarize the distribution for a variable or response and check assumptions before performing a statistical test. Graphs you might need to examine include time plots for data collected over time and QQ plots for checking whether a normal (bell-curve) model is a reasonable distribution for a quantitative variable. These techniques can be very useful at the start of data analysis to get a feel for the data. Application:Brad is the manager of the Detroit Tigers and to prepare for the next round of the playoffs, he would like to run a hypothesis test involving the mean number of runs his players have scored over the last month of play. Brad knows that one assumption required for performing this analysis about the mean is that his data must be considered a random sample (the observations can be viewed as coming from the same parent population). He can examine this assumption by collecting the number of runs scored over the last month and creating a time plot. Overview:Data on a quantitative variable should be examined graphically. If the data has been collected over time, the first graph to examine is a time plot. If the resulting time plot appears to be stable, or if the data was not collected over time, then graphs that can be used to summarize the distribution for a single quantitative variable or response are a histogram, a boxplot, and perhaps a QQ plot. Each graph provides different information about the distribution. The overall shape of the distribution and existence of outliers can generally be used to assess if the data appear to be coming from a relatively homogenous population. If so, then various numerical summariesmay be used to characterize the center of the distribution and the spread of the distribution. Note that some graphical tools are introduced solely in lab, not in lecture, so it will benefit you to read this overview thoroughly Sequence (Time) Plots:Data might be gathered over time. Employment rate, stock prices, and sales figures are just a few examples. When data is gathered over time, such as the number of runs scored over a one month by the Tigers, it is generally wise to examine the data plotted against time. Plots against time can reveal the main features of a time series, overall patterns and striking deviation from those patterns. Some overall patterns that may arise are: A persistent, long-term rise or fall called a trend(either increasing or decreasing). A persistent, long-term increase or decrease in the variationof the observations called a pattern in variation. A pattern that repeats itself at regular intervals of time (i.e. influenced by seasonal factors such as month or day of week) is called seasonal variation.